In [1]:

    

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import scipy.signal


    

In [2]:

    

x = np.fromfile('bits_800bps.f32', dtype = 'float32')[20000:]
off = 2
z = x[off:x.size//8*8+off].reshape((-1,8))


    

In [3]:

    

plt.figure(figsize = (10,6), facecolor = 'w')
plt.plot(x, '.')
plt.ylabel('Amplitude')
plt.title('Soft symbols')
plt.xlabel('Symbol');


    

In [4]:

    

plt.figure(figsize = (10,6), facecolor = 'w')
plt.plot(np.average(z, axis = 0), '.-')
plt.title('Averages of each frame bit')
plt.ylabel('Amplitude')
plt.xlabel('Frame bit');


    

In [5]:

    

plt.figure(figsize = (10,6), facecolor = 'w')
for j in range(1,6):
    corr = scipy.signal.correlate(z[:,j], z[:,j], mode = 'full')
    plt.plot(corr[corr.size//2:][:35], label = f'Frame bit {j}')
plt.title('Autocorrelation of each frame bit sequence')
plt.ylabel('Amplitude')
plt.xlabel('Lag (symbols)')
plt.legend();


    

In [6]:

    

plt.plot(-z[:,6] * z[:,4], '.')


    

    
Out[6]:





[<matplotlib.lines.Line2D at 0x7f1d22100490>]






    

In [7]:

    

b = -z[:,7] * z[:,3] # note bit 3 instead of 2


    

In [8]:

    

np.where(np.convolve(np.all(np.sign(z[:,(1,5)]) == [1,1], axis = 1), np.ones(5)) == 5)


    

    
Out[8]:





(array([  283,  1083,  1883,  2683,  3483,  4283,  5083,  5883,  6683,
         7483,  8283,  9083,  9883, 10683, 11483, 12283, 13083, 13883,
        14683, 15483, 16283, 17083, 17883, 18683, 19483, 20283, 21083,
        21883, 22683, 23483, 24283, 25083, 25883, 26683, 27483, 28283,
        29083, 29883, 30683, 31483, 32283, 33083, 33883, 34683, 35483,
        36283, 37083, 37883, 38683, 39483, 40283, 41083, 41883, 42683,
        43483, 44283, 45083, 45883, 46683, 47483, 48283, 49083, 49883,
        50683, 51483, 52283, 53083, 53883, 54683, 55483, 56283, 57083,
        57883, 58683, 59483, 60283, 61083, 61883, 62683, 63483, 64283,
        65083, 65883, 66683, 67483, 68283, 69083, 69883, 70683, 71483,
        72283, 73083, 73883, 74683, 75483, 76283, 77083, 77883]),)

In [9]:

    

z[283-4:284,(1,5)]


    

    
Out[9]:





array([[0.9908856, 1.1165041],
       [1.0083642, 1.1007323],
       [1.15526  , 1.6971315],
       [0.8049949, 1.1295491],
       [0.8837602, 0.9101658]], dtype=float32)

In [10]:

    

framestart = 284-1


    

In [11]:

    

bb = 1*(b[framestart:] > 0)
bb = bb[:bb.size//200*200].reshape((-1,200))


    

In [12]:

    

plt.figure(figsize = (14,10))
plt.imshow(bb, aspect = 0.3)


    

    
Out[12]:





<matplotlib.image.AxesImage at 0x7f1d22196650>






    

In [13]:

    

plt.figure(figsize = (14,10))
plt.imshow(bb[:,::2], aspect = 0.15)


    

    
Out[13]:





<matplotlib.image.AxesImage at 0x7f1d3c0794d0>






    

In [14]:

    

plt.figure(figsize = (14,10))
plt.imshow(bb[:,1::2], aspect = 0.15)


    

    
Out[14]:





<matplotlib.image.AxesImage at 0x7f1d2209ee10>






    

In [15]:

    

seconds = (np.packbits(bb[:,23*2:27*2:2], axis = 1).ravel() >> 4).astype('int')
ten_seconds = (np.packbits(bb[:,20*2:23*2:2], axis = 1).ravel() >> 5).astype('int')
minutes = (np.packbits(bb[:,16*2:20*2:2], axis = 1).ravel() >> 4).astype('int')
ten_minutes = (np.packbits(bb[:,13*2:16*2:2], axis = 1).ravel() >> 5).astype('int')

np.diff(seconds + 10 * ten_seconds + 60 * minutes + 600 * ten_minutes)


    

    
Out[15]:





array([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])

In [16]:

    

conv_input = bb[0,::2]
conv_output = bb[0, 1::2]


    

In [17]:

    

np.where(conv_output)[0][-1] - np.where(conv_input)[0][-1]


    

    
Out[17]:





9

In [18]:

    

l = 10


    

In [19]:

    

A = np.zeros((10,10), dtype = 'int')
b = np.zeros((10,1), dtype = 'int')


    

In [20]:

    

for n,k in enumerate(range(7,17)):
    j = k - 10
    t = 0
    if j < 0:
        j = 0
        t = 10 - k
    A[n,t:] = conv_input[j:k]
    b[n] = conv_output[k-1]


    

In [21]:

    

p = np.linalg.solve(A, b).astype('int').ravel() % 2
p


    

    
Out[21]:





array([1, 0, 0, 1, 1, 0, 0, 1, 1, 1])

In [22]:

    

np.all(np.convolve(conv_input, p[::-1])[:conv_output.size] % 2 == conv_output)


    

    
Out[22]:





True

In [23]:

    

np.all([np.all(np.convolve(bb[j,::2], p[::-1])[:bb.shape[1]//2] % 2 == bb[j,1::2]) for j in range(bb.shape[0])])


    

    
Out[23]:





True